Zobrazeno 1 - 10
of 221
pro vyhledávání: '"Lack, Stephen"'
Autor:
Bourke, John, Lack, Stephen
Recently Riehl and Verity have introduced $\infty$-cosmoi, which are certain simplicially enriched categories with additional structure. In this paper we investigate those $\infty$-cosmoi which are in fact $2$-categories; we shall refer to these as $
Externí odkaz:
http://arxiv.org/abs/2305.16002
Autor:
Lack, Stephen, Tendas, Giacomo
Publikováno v:
Journal of Pure and Applied Algebra, 228(2):107444, 2024
In this paper we characterize those accessible $\mathcal V$-categories that have limits of a specified class. We do this by introducing the notion of companion $\mathfrak C$ for a class of weights $\Psi$, as a collection of special types of colimit d
Externí odkaz:
http://arxiv.org/abs/2212.07135
Autor:
Fujii, Soichiro, Lack, Stephen
Publikováno v:
Theory and Applications of Categories, 40(14), pp 390-412, 2024
We show that 2-categories of the form $\mathscr{B}\mbox{-}\mathbf{Cat}$ are closed under slicing, provided that we allow $\mathscr{B}$ to range over bicategories (rather than, say, monoidal categories). That is, for any $\mathscr{B}$-category $\mathb
Externí odkaz:
http://arxiv.org/abs/2211.12122
Autor:
Lack, Stephen, Miranda, Adrian
Publikováno v:
Theory and Applications of Categories, Vol. 42, 2024, No. 1, pp 2-18
For a 2-category $\mathcal{K}$, we consider Street's 2-category Mnd($\mathcal{K}$) of monads in $\mathcal{K}$, along with Lack and Street's 2-category EM($\mathcal{K}$) and the identity-on-objects-and-1-cells 2-functor Mnd($\mathcal{K}$) $\to$ EM($\m
Externí odkaz:
http://arxiv.org/abs/2211.02210
Autor:
Lack, Stephen, Tendas, Giacomo
Publikováno v:
Journal of Pure and Applied Algebra, 227(2):107196, 2023
We provide a new characterization of enriched accessible categories by introducing the two new notions of virtual reflectivity and virtual orthogonality as a generalization of the usual reflectivity and orthogonality conditions for locally presentabl
Externí odkaz:
http://arxiv.org/abs/2205.11056
Autor:
Bourke, John, Lack, Stephen
Publikováno v:
In Journal of Pure and Applied Algebra September 2024 228(9)
Autor:
Bourke, John, Lack, Stephen
Publikováno v:
Journal of Pure and Applied Algebra 227 (2023) 107255
We introduce the notion of an accessible $\infty$-cosmos and prove that these include the basic examples of $\infty$-cosmoi and are stable under the main constructions. A consequence is that the vast majority of known examples of $\infty$-cosmoi are
Externí odkaz:
http://arxiv.org/abs/2111.00147
Autor:
Lack, Stephen, Tendas, Giacomo
Publikováno v:
Advances in Mathematics, Volume 404, Part A, 6 August 2022, 108381
The importance of accessible categories has been widely recognized; they can be described as those freely generated in some precise sense by a small set of objects and, because of that, satisfy many good properties. More specifically finitely accessi
Externí odkaz:
http://arxiv.org/abs/2107.08612
Autor:
Lack, Stephen, Tendas, Giacomo
Publikováno v:
In Journal of Pure and Applied Algebra February 2024 228(2)
Publikováno v:
Advances in Mathematics 412 (2023) 108812
We prove an adjoint functor theorem in the setting of categories enriched in a monoidal model category $\mathcal V$ admitting certain limits. When $\mathcal V$ is equipped with the trivial model structure this recaptures the enriched version of Freyd
Externí odkaz:
http://arxiv.org/abs/2006.07843